Abstract
Parametric timed automata (PTAs) are a powerful formalism to reason about, model and verify real-time systems in which some constraints are unknown, or subject to uncertainty. In the literature, PTAs come in several variants: in particular the domain of parameters can be integers or rationals, and can be bounded or not. Also clocks can either be compared only to a single parameter, or to more complex linear expressions. Yet we do not know how these variants compare in terms of expressiveness, and even the notion of expressiveness for parametric timed models does not exist in the literature. Furthermore, since most interesting problems are undecidable for PTAs, subclasses, such as L/U-PTAs, have been proposed for which some of those problems are decidable. It is not clear however what can actually be modeled with those restricted formalisms and their expressiveness is thus a crucial issue. We therefore propose two definitions for the expressiveness of parametric timed models: the first in terms of all the untimed words that can be generated for all possible valuations of the parameters, the second with the additional information of which parameter valuations allow which word, thus more suitable for synthesis issues. We then use these two definitions to propose a first comparison of the aforementioned PTA variants.
This work is partially supported by the ANR national research program “PACS” (ANR-14-CE28-0002).
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- 1.
Technically, \(v_{0/\infty }\) is not a parameter valuation, as the definition of valuation does not allow \(\infty \). However, we will use it only to valuate an L/U-PTA (or an hL/U-PTA) with it; observe that valuating an L/U-PTA with \(v_{0/\infty }\) still gives a valid TA.
- 2.
Comparing constrained languages would make no sense since obviously the parameter valuations cannot match in general in the rational and integer settings.
References
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Alur, R., Henzinger, T.A., Vardi, M.Y.: Parametric real-time reasoning. In: STOC, pp. 592–601. ACM (1993)
André, É.: What’s decidable about parametric timed automata? In: Artho, C., et al. (eds.) FTSCS 2015. CCIS, vol. 596, pp. 52–68. Springer, Heidelberg (2016). doi:10.1007/978-3-319-29510-7_3
André, É., Fribourg, L.: Behavioral cartography of timed automata. In: Kučera, A., Potapov, I. (eds.) RP 2010. LNCS, vol. 6227, pp. 76–90. Springer, Heidelberg (2010)
André, É., Markey, N.: Language preservation problems in parametric timed automata. In: Sankaranarayanan, S., Vicario, E. (eds.) FORMATS 2015. LNCS, vol. 9268, pp. 27–43. Springer, Heidelberg (2015)
Beneš, N., Bezděk, P., Larsen, K.G., Srba, J.: Language emptiness of continuous-time parametric timed automata. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 69–81. Springer, Heidelberg (2015)
Bérard, B., Petit, A., Diekert, V., Gastin, P.: Characterization of the expressive power of silent transitions in timed automata. Fundamenta Informaticae 36(2–3), 145–182 (1998)
Bozzelli, L., La Torre, S.: Decision problems for lower/upper bound parametric timed automata. Formal Meth. Syst. Des. 35(2), 121–151 (2009)
Bundala, D., Ouaknine, J.: Advances in parametric real-time reasoning. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014, Part I. LNCS, vol. 8634, pp. 123–134. Springer, Heidelberg (2014)
Doyen, L.: Robust parametric reachability for timed automata. Inf. Process. Lett. 102(5), 208–213 (2007)
Hune, T., Romijn, J., Stoelinga, M., Vaandrager, F.W.: Linear parametric model checking of timed automata. J. Logic Algebraic Program. 52–53, 183–220 (2002)
Jovanović, A., Lime, D., Roux, O.H.: Integer parameter synthesis for timed automata. Trans. Softw. Eng. 41(5), 445–461 (2015)
Miller, J.S.: Decidability and complexity results for timed automata and semi-linear hybrid automata. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 296–309. Springer, Heidelberg (2000)
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André, É., Lime, D., Roux, O.H. (2016). On the Expressiveness of Parametric Timed Automata. In: Fränzle, M., Markey, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2016. Lecture Notes in Computer Science(), vol 9884. Springer, Cham. https://doi.org/10.1007/978-3-319-44878-7_2
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